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Thus, the Fisher information may be seen as the curvature of the support curve (the graph of the log-likelihood). Near the maximum likelihood estimate, low Fisher information therefore indicates that the maximum appears "blunt", that is, the maximum is shallow and there are many nearby values with a similar log-likelihood. Conversely, high ...
A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
[1] [3] [6] It is shown that the quantum Fisher information can also be a sensitive probe of a quantum phase transition (e.g. recognizing the superradiant quantum phase transition in the Dicke model [6]). The quantum Fisher information [,] of a state with respect to the observable is defined as
In information geometry, the Fisher information metric [1] is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability distributions. It can be used to calculate the distance between probability distributions. [2] The metric is interesting in several aspects.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
Subsequently, Nachtergaele and Sims [12] extended the results of [9] to include models on vertices with a metric and to derive exponential decay of correlations. From 2005 to 2006 interest in Lieb–Robinson bounds strengthened with additional applications to exponential decay of correlations (see [ 2 ] [ 5 ] [ 13 ] and the sections below).
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
The choice R(u) = u(1 − u) yields Fisher's equation that was originally used to describe the spreading of biological populations, [3] the Newell–Whitehead-Segel equation with R(u) = u(1 − u 2) to describe Rayleigh–Bénard convection, [4] [5] the more general Zeldovich–Frank-Kamenetskii equation with R(u) = u(1 − u)e-β(1-u) and 0 ...